Learning correlated equilibria in population games

Abstract

The paper develops a framework for the analysis of finite n-player games, recurrently played by randomly drawn n-tuples of players, from a finite population. We first relate the set of equilibria of this game to the set of correlated equilibria of the underlying game, and then focus on learning processes modelled as Markovian adaptive dynamics. For the class of population games for which the underlying game has identical interests, we show that, independently of the matching technology, any myopic-best reply dynamics converges (in probability) to a correlated equilibrium. We also analyze noisy best reply dynamics, where players’ behaviour is perturbed by payoff-dependent mistakes, and explicitly characterize the limit distribution of the perturbed game in terms of the correlated equilibrium payoff of the underlying game.